Search results for " optimization"
showing 10 items of 2367 documents
Solving chance constrained optimal control problems in aerospace via Kernel Density Estimation
2017
International audience; The goal of this paper is to show how non-parametric statistics can be used to solve some chance constrained optimization and optimal control problems. We use the Kernel Density Estimation method to approximate the probability density function of a random variable with unknown distribution , from a relatively small sample. We then show how this technique can be applied and implemented for a class of problems including the God-dard problem and the trajectory optimization of an Ariane 5-like launcher.
A combination of algebraic, geometric and numerical methods in the contrast problem by saturation in magnetic resonance imaging
2014
In this article, the contrast imaging problem by saturation in nuclear magnetic resonance is modeled as a Mayer problem in optimal control. The optimal solution can be found as an extremal solution of the Maximum Principle and analyzed with the recent advanced techniques of geometric optimal control. This leads to a numerical investigation based on shooting and continuation methods implemented in the HamPath software. The results are compared with a direct approach to the optimization problem and implemented within the Bocop toolbox. In complement lmi techniques are used to estimate a global optimum. It is completed with the analysis of the saturation problem of an ensemble of spin particle…
Minimum Time Control of the Restricted Three-Body Problem
2012
The minimum time control of the circular restricted three-body problem is considered. Controllability is proved on an adequate submanifold. Singularities of the extremal flow are studied by means of a stratification of the switching surface. Properties of homotopy maps in optimal control are framed in a simple case. The analysis is used to perform continuations on the two parameters of the problem: The ratio of the masses, and the magnitude of the control.
Enhancement and assessment of WKS variance parameter for intelligent 3D shape recognition and matching based on MPSO
2016
This paper presents an improved wave kernel signature (WKS) using the modified particle swarm optimization (MPSO)-based intelligent recognition and matching on 3D shapes. We select the first feature vector from WKS, which represents the 3D shape over the first energy scale. The choice of this vector is to reinforce robustness against non-rigid 3D shapes. Furthermore, an optimized WKS-based method for extracting key-points from objects is introduced. Due to its discriminative power, the associated optimized WKS values with each point remain extremely stable, which allows for efficient salient features extraction. To assert our method regarding its robustness against topological deformations,…
Drivers-Inspired Ants for Solving the Vehicle Routing Problem with Time Windows
2016
International audience; In our study, we develop a method that merges two information sources within ants colony optimization heuristic. Namely artificial ants which occurs for short term optimization and transporter's vehicles that occurs in long term and continuous optimization toward solving the real-world vehicle routing problem. This study is supported by a transporter (Upsilon) of the region of l'Yonne in France and a transport and logistics software development company (Tedies). Our method suits for transporters that use human planners to make decisions about their tours and intending to move to computer planners without drastically upsetting the drivers habits. Hence, the pledge of …
Scheduling independent stochastic tasks under deadline and budget constraints
2018
This article discusses scheduling strategies for the problem of maximizing the expected number of tasks that can be executed on a cloud platform within a given budget and under a deadline constraint. The execution times of tasks follow independent and identically distributed probability laws. The main questions are how many processors to enroll and whether and when to interrupt tasks that have been executing for some time. We provide complexity results and an asymptotically optimal strategy for the problem instance with discrete probability distributions and without deadline. We extend the latter strategy for the general case with continuous distributions and a deadline and we design an ef…
Robust control of networks under discrete disturbances and controls
2011
We consider dynamic networks where the disturbances and control actions take discrete values. We briefly survey some of our recent results establishing necessary and sufficient conditions for the existence of robustly globally invariant (hyper box) sets, as well as sufficient conditions for global attractivity of such sets.We then establish connections between these results and existing results in the literature for the setup where all the inputs are analog. Finally, we derive tight upper and lower bounds on the smallest such set in the special case of a degenerate network.
Étude de statistiques combinatoires et de leur impact en optimisation évolutionnaire
2021
This thesis studies combinatorial objects, with both an algorithmic and a combinatorial point of view. In the combinatorial part, we take care first, the enumeration of Catalan words avoiding pairs of patterns of length three, presenting the proofs of each case with various enumeration methods. Catalan words are particular growth-restricted words counted by the eponymous integer sequence. More precisely, we systematically explore the structural properties of the sets of words under consideration and give enumerating results by constructive bijections or bivariate generating functions with respect to the length and descent number. Then, we study a sorting machine using two stacks in s…
Refitting solutions promoted by $\ell_{12}$ sparse analysis regularization with block penalties
2019
International audience; In inverse problems, the use of an $\ell_{12}$ analysis regularizer induces a bias in the estimated solution. We propose a general refitting framework for removing this artifact while keeping information of interest contained in the biased solution. This is done through the use of refitting block penalties that only act on the co-support of the estimation. Based on an analysis of related works in the literature, we propose a new penalty that is well suited for refitting purposes. We also present an efficient algorithmic method to obtain the refitted solution along with the original (biased) solution for any convex refitting block penalty. Experiments illustrate the g…
Cut-off method for endogeny of recursive tree processes
2016
Given a solution to a recursive distributional equation, a natural (and non-trivial) question is whether the corresponding recursive tree process is endogenous. That is, whether the random environment almost surely defines the tree process. We propose a new method of proving endogeny, which applies to various processes. As explicit examples, we establish endogeny of the random metrics on non-pivotal hierarchical graphs defined by multiplicative cascades and of mean-field optimization problems as the mean-field matching and travelling salesman problems in pseudo-dimension q>1.